This is the full statute where I've bolded/italicized important lines relevant to the thread. The tricky part of the law, IMO, is section (b) which states that vehicles driving slower than the "normal speed" of other vehicles shall stay in the right hand lane. Predominantly this would apply to people driving below the speed limit, maybe due to a heavy load, car issues, etc., but could potentially be enforced to supplement the absence of the "left lane passing only" law on roadways with more than two lanes in one direction. Regardless of anyone's interpretation of any of these laws, they are rarely, if at all, enforced.
Sec. 545.051. DRIVING ON RIGHT SIDE OF ROADWAY.
(a) An operator on a roadway of sufficient width shall drive on the right half of the roadway, unless :
(1) the operator is passing another vehicle;
(2) an obstruction necessitates moving the vehicle left of the center of the roadway and the operator yields the right-of-way to a vehicle that:
(A) is moving in the proper direction on the unobstructed portion of the roadway; and
(B) is an immediate hazard;
(3) the operator is on a roadway divided into three marked lanes for traffic; or
(4) the operator is on a roadway restricted to one-way traffic.
(b) An operator of a vehicle on a roadway moving more slowly than the normal speed of other vehicles at the time and place under the existing conditions shall drive in the right-hand lane available for vehicles, or as close as practicable to the right-hand curb or edge of the roadway, unless the operator is:
(1) passing another vehicle; or
(2) preparing for a left turn at an intersection or into a private road or driveway.
(c) An operator on a roadway having four or more lanes for moving vehicles and providing for two-way movement of vehicles may not drive left of the center line of the roadway except:
(1) as authorized by an official traffic-control device designating a specified lane to the left side of the center of the roadway for use by a vehicle not otherwise permitted to use the lane;
(2) under the conditions described by Subsection (a)(2); or
(3) in crossing the center line to make a left turn into or out of an alley, private road, or driveway.